Tuning Contact Angles of Aqueous Droplets on Hydrophilic and Hydrophobic Surfaces by Surfactants

Adsorption of small amphiphilic molecules occurs in various biological and technological processes, sometimes desired while other times unwanted (e.g., contamination). Surface-active molecules preferentially bind to interfaces and affect their wetting properties. We use molecular dynamics simulations to study the adsorption of short-chained alcohols (simple surfactants) to the water–vapor interface and solid surfaces of various polarities. With a theoretical analysis, we derive an equation for the adsorption coefficient, which scales exponentially with the molecular surface area and the surface wetting coefficient and is in good agreement with the simulation results. We apply the outcomes to aqueous sessile droplets containing surfactants, where the competition of surfactant adsorptions to both interfaces alters the contact angle in a nontrivial way. The influence of surfactants is the strongest on very hydrophilic and hydrophobic surfaces, whereas droplets on moderately hydrophilic surfaces are less affected.


S1. COMPOSITION OF SIMULATED SYSTEMS
Tables S1-S6 provide the compositions of the simulated systems in terms of the number of used alcohol and water molecules as well as the resulting alcohol concentrations c 0 in the bulk region.

S2. RELATION BETWEEN THE POLARITY RESCALING FACTOR AND THE WATER CONTACT ANGLE OF THE SAM
We tuned the hydrophobicity of the SAM by rescaling the original partial charges in the OH groups. The relation between the rescaling factor, the contact angle of water droplets, and its cosine is shown in Figure S1.

S3. DEPENDENCE OF SURFACE TENSION ON CONCENTRATION
We express eq 6 in the main text in terms of bulk surfactant concentration, obtaining which in the linear form becomes Both equations are used in Figure S2, showing ∆γ as a function of c 0 . The theoretical and MD values are compared with experimental data. The comparison shows decent agreement of the simulation data with experimental results, especially for propanol and pentanol. Linear fits (eq S2) to the experimental data give K v = 2.1 nm for methanol, K v = 19 nm for propanol, and K v = 290 nm for pentanol.

S4. KIRKWOOD-BUFF INTEGRALS
To calculate the bulk properties necessary for the Kirkwood-Buff (KB) theory used in Section 3.1, we simulated three independent realizations of a homogeneous system in a cubic simulation box of edge 5 nm in the NPT ensemble for 100 ns for each concentration of surfactant. From the simulations, we extracted the radial distribution functions g mw (r) and g mm (r), shown in Figure S3, and use them in eq 5 to calculate the KB integrals, G mw and G mm , shown in Figure S4 as a function of surfactant concentration. Both G mw and G mm are independent of concentration at low concentrations (within the numerical uncertainty), which justifies our approximation in the main text.

S5. SECOND-ORDER VIRIAL EXPANSION
To rationalize the theoretical deviations from simulations observed in Figures 3 and 4, we quantified the interaction between surfactant molecules at the water-vapor interface and estimate its effect on adsorption isotherms. To that end, we simulated two surfactant molecules at a water-vapor interface for 70 ns. The two molecules were weakly restrained to the water-vapor interface by harmonic potentials of strength 3.011 mN/m in z-direction in order to prevent them from leaving the interface and simplify the analysis. From the simulations, we evaluated the two-dimensional radial distribution function between both surfactant molecules g (2D) mm (r) in the plane of the interface (shown in Figure S5), and used it to calculate the two-dimensional second virial coefficient The resulting numerical values of B (2D) 2 are 0.026±0.008 nm 2 for methanol, −0.16 ± 0.11 nm 2 for propanol, and −0.64 ± 0.11 nm 2 for pentanol. The negative signs in the latter two indicate the effective surfactant-surfactant attraction at the water-vapor interface. In the second-order virial expansion (valid for B (2D) 2 Γ ≪ 1), the excess adsorption is given by 6 (S4) Figure S6 shows MD data for adsorption (similar to Figure 3 in the main text, but the fits of Henry's law involve only the first five data points). The resulting K v values, which slightly differ from those calculated from the Langmuir fit, are used in eq S4, shown as dashed lines. Because of B (2D) 2 < 0 for propanol and pentanol, the predicted adsorption curves bend upwards. This can qualitatively explain the distinct trend for pentanol at intermediate concentrations, which features upward concavity prior to saturation at higher concentrations.

Equation S4
can now be used with the formalism of the Gibbs adsorption isotherm to calculate the surface tension reduction expressed by Γ, which resembles the pressure of 2D gas in the classical virial expansion. For propanol and pentanol, the correction is positive, meaning smaller reduction in γ. Figure S7 shows the surface tension reduction versus Γ (similar to Figure 4 in the main text), where the predictions of eq S5 are shown by dashdotted lines. The predictions capture well the intermediate concentrations. This implies that the observed deviations from eq 6 (based on fitting the Langmuir isotherm) can be ascribed to attraction and cluster formation of surfactants at the interface.  (c) pentanol Figure S6: Adsorption Γ at the water-vapor interface as a function of the bulk concentration of (a) methanol, (b) propanol, and (c) pentanol (same MD data as in Figure 3 in the main text). Here, Henry's law is fitted to the first 5 data points (dashed lines), and the obtained Kv (0.76 nm for methanol, 12.9 nm for propanol, and 154 nm for pentanol) is used to plot the second-order virial correction given by eq S4 (dash-dotted lines). For comparison, fits of the Langmuir isotherm (eq 2) are shown as green lines.  Figure S7: Reduction of the water-vapor surface tension versus adsorption as obtained from MD simulations (symbols) and theoretical predictions: eq 6 (solid lines), its linear expansion eq 8 (dotted line), and the second-order virial expansion eq S5 (dash-dotted lines).

S6. ADSORPTION TO SOLID SURFACES
In Figure S8, we show rescaled density profiles (as in Figure  5b in the main text), highlighting the penetration of alcohols into the surface. In Figures S9, S10, and S11, we show the comparison between MD simulations results and the Langmuir (eq 2) and Henry (eq 3) isotherms for the surfaces not shown in Figure 6. The parameters of the Langmuir isotherm, Γ ∞ and k c , were fitted, while the coefficient K s for Henry's law was calculated from the fitted parameters as K s = Γ ∞ k c . The fitting results are shown in Figures 7 and S12.

S7. ESTIMATING SURFACTANT ADSORPTION AT THE SOLID-VAPOR INTERFACE
To check that there is no adsorption at the solid-vapor interface, we perform simulations of a cylindrical surfactantcontaining water droplet on the solid surface. The surface is the same as in the main simulations but twice as long in the y-direction. The droplet is periodically replicated along the x-direction, as shown in Figure S13. Averaging the densities over time and x-direction, we obtain the yz-resolved surfactant density profile, which is shown in Figure S14. From the obtained density plots of all three surfactants, it is possible to see that the density at the solidvapor interface remains zero, which justifies our assumption.